fix: route background memory review by destination

[nicha16]

Summary

• Make background memory review destination-first
• Route stable user facts, assistant/environment facts, reusable procedures, and session-only task history to the right stores
• Update prompt tests for the narrower memory admission behavior

Test plan

• python -m pytest tests/run_agent/test_background_review.py tests/run_agent/test_review_prompt_class_first.py -q -o 'addopts='

[teknium1]

Thanks for the focused memory-routing change. The underlying issue remains on current main: agent/background_review.py:160-168 and agent/background_review.py:276-281 still use broad admission wording, while tools/memory_tool.py:1076-1086 already defines the narrower USER.md/MEMORY.md/skip contract.

Problems

• The prompt definitions were moved from run_agent.py to agent/background_review.py by d35ee7bc; run_agent.py:1576-1582 now only re-exports them. The current PR is therefore dirty against main and its implementation hunk cannot be applied at the original location.

Suggested changes

• Transplant the prompt and test intent to agent/background_review.py, keeping the routing language aligned with tools/memory_tool.py:1076-1086.

Automated hermes-sweeper review.

[teknium1]

Current main moved these prompt definitions to agent/background_review.py in d35ee7bc; run_agent.py:1576-1582 now only re-exports them. Please salvage this hunk at the active source location so the routing change reaches the prompt used by the background-review thread.